Abstract: |
The Hessenberg varieties are certain subvarieties of the complete flag variety $Fl_n$.They are associated with a Hessenberg graph and an element $h \in GL(n)$, and have many interesting application to representation theory, combinatorics among many others branches of Mathematics. In my talk I introduce a family of certain noncommutative algebras together with distinguish commutative subalgebra(s) inside each. The main goal of my talk is to describe relations in that commutative algebras, and for Hessenberg graphs the former are isomorphic to the cohomology ring of the latter. Finally I state Conjecture concerning the structure of the cohomology theories of regular nilpotent Hessenberg varieties, which are associated with multiplicative formal group laws (K-theory) and the Hirzebruch formal groups (H-theories). |